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A canonical G_m (or G) action on the Slodowy slice

Question By Slodowy slice I mean a transverse slice at a subregular nilpotent orbit in a simple Lie algebra $\mathfrak{g}$ (in particular I am not intersecting with the nilpotent cone). Consider the ...
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Why transverse slices?

I would like to know why people are interested in transverse slices. In particular, I would like to know why people study the Slodowy slice to orbits in the nilpotent cone. In Chriss and Ginzburg's ...
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Slodowy slices for two-block nilpotents

My question is about an isomorphism between two varieties of the form discussed in this thread; it is also related to an earlier question of mine. Let $z_n$ be the standard nilpotent of type $(n,n)$. ...
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Regular Functions on Slodowy Slices

I recently learned that there is a natural identification, given a simple Lie algebra, Polynomial functions on the Slodowy slice of a regular nilpotent orbit $\simeq$ polynomial functions on the ...
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Does the preimage of the Slodowy slice in $T^*G/P$ have a name?

Let $G$ be your favorite simple complex Lie group, and $P\subset G$ your favorite parabolic subgroup. We can identify $T^*G/P$ with the space of pairs $$\{(gP,x)\in G/P\times \mathfrak g | x\perp ...